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Stabilization of a nonlinear rotating disk-beam system with localized thermal effect

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Abstract

This article considers the stabilization problem of a rotating disk-beam system with localized thermal effect and torque control. Assume that the disk rotates with nonuniform angular velocity. A subdomain of the elastic beam is with thermoelastic damping, which is a kind of intrinsic one since thermoelasticity exists in almost all materials. Using only torque control, we prove that the system can be stabilized exponentially under certain condition on angular velocity, no matter how small the part with thermal effect of the beam is. The exponential stability is proved mainly by the resolvent estimate. Some numerical simulations are further given to support the theoretical results obtained in this paper.

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Acknowledgements

The authors would like to thank the anonymous referees for their helpful comments and suggestions.

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Authors and Affiliations

  1. School of Mathematics, Tianjin University, Tianjin, 300354, China

    Huan Geng, Zhong-Jie Han, Jing Wang & Gen-Qi Xu

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  1. Huan Geng
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  2. Zhong-Jie Han
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  3. Jing Wang
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  4. Gen-Qi Xu
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Correspondence to Zhong-Jie Han.

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The authors declare that they have no conflict of interest.

Additional information

This research is supported by the Natural Science Foundation of China Grant NSFC-61573252, 61174080.

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Geng, H., Han, ZJ., Wang, J. et al. Stabilization of a nonlinear rotating disk-beam system with localized thermal effect. Nonlinear Dyn 93, 785–799 (2018). https://doi.org/10.1007/s11071-018-4227-9

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  • DOI: https://doi.org/10.1007/s11071-018-4227-9

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